Moreover, considering linear fluid equations in moving domain from the uncertainty quantification point of view would be another interesting problem to study, in particular from the application perspective [1]}, [2]}. The uncertainty of the initial data is then model as a random variable. Especially it would be interesting to consider the equations on the random moving domain. These type of problems were already considered by one of the authors for elliptic PDEs on curved domain [3]} and for linear parabolic equations on random domains [4]}, where the study of parabolic Stokes equation on moving domain was also mentioned. Exploiting our well-posedness result and following the ideas from [4]}, one could extend our results to the case of a random domain. However, this will not be considered in details in this paper and is left for the future consideration.
